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+
+ <p>The transformations are intended to map parameters that should only take
+ on restricted values to the full scale of real numbers. For kinetic rate
+ constants and other paramters that can only take on positive values, a
+ simple log transformation is used. For compositional parameters, such as
+ the formations fractions that should always sum up to 1 and can not be
+ negative, the <code>ilr</code> transformation is used.</p>
+
+ <p>The transformation of sets of formation fractions is fragile, as it supposes
+ the same ordering of the components in forward and backward transformation.
+ This is no problem for the internal use in <code>mkinfit</code>.</p>
+
+
+ <pre><span class='fu'>transform_odeparms</span>(<span class='no'>parms</span>, <span class='no'>mkinmod</span>,
+ <span class='kw'>transform_rates</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>transform_fractions</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
+<span class='fu'>backtransform_odeparms</span>(<span class='no'>transparms</span>, <span class='no'>mkinmod</span>,
+ <span class='kw'>transform_rates</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>transform_fractions</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</pre>
+
+ <h2>Arguments</h2>
+ <dl class="dl-horizontal">
+ <dt>parms</dt>
+ <dd>
+ Parameters of kinetic models as used in the differential equations.
+ </dd>
+ <dt>transparms</dt>
+ <dd>
+ Transformed parameters of kinetic models as used in the fitting procedure.
+ </dd>
+ <dt>mkinmod</dt>
+ <dd>
+ The kinetic model of class <code>mkinmod</code>, containing the names of
+ the model variables that are needed for grouping the formation fractions
+ before <code>ilr</code> transformation, the parameter names and
+ the information if the pathway to sink is included in the model.
+ </dd>
+ <dt>transform_rates</dt>
+ <dd>
+ Boolean specifying if kinetic rate constants should be transformed in the
+ model specification used in the fitting for better compliance with the
+ assumption of normal distribution of the estimator. If TRUE, also
+ alpha and beta parameters of the FOMC model are log-transformed, as well
+ as k1 and k2 rate constants for the DFOP and HS models and the break point tb
+ of the HS model.
+ </dd>
+ <dt>transform_fractions</dt>
+ <dd>
+ Boolean specifying if formation fractions constants should be transformed in the
+ model specification used in the fitting for better compliance with the
+ assumption of normal distribution of the estimator. The default (TRUE) is
+ to do transformations. The g parameter of the DFOP and HS models are also
+ transformed, as they can also be seen as compositional data. The
+ transformation used for these transformations is the <code>ilr</code>
+ transformation.
+ </dd>
+ </dl>
+
+ <div class="Value">
+ <h2>Value</h2>
+
+ <p>A vector of transformed or backtransformed parameters with the same names
+ as the original parameters.</p>
+ </div>
+
+ <h2 id="examples">Examples</h2>
+ <pre class="examples"><div class='input'><span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinmod</span>(
+ <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>, <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
+ <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>))</div><div class='output'><strong class='text-info'>Successfully compiled differential equation model from auto-generated C code.</strong></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span>
+<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
+<span class='fu'>summary</span>(<span class='no'>fit</span>, <span class='kw'>data</span><span class='kw'>=</span><span class='fl'>FALSE</span>) <span class='co'># See transformed and backtransformed parameters</span></div><div class='output co'>#&gt; mkin version: 0.9.44.9000
+#&gt; R version: 3.3.1
+#&gt; Date of fit: Thu Oct 6 09:18:08 2016
+#&gt; Date of summary: Thu Oct 6 09:18:08 2016
+#&gt;
+#&gt; Equations:
+#&gt; d_parent = - k_parent_sink * parent - k_parent_m1 * parent
+#&gt; d_m1 = + k_parent_m1 * parent - k_m1_sink * m1
+#&gt;
+#&gt; Model predictions using solution type deSolve
+#&gt;
+#&gt; Fitted with method Port using 153 model solutions performed in 0.636 s
+#&gt;
+#&gt; Weighting: none
+#&gt;
+#&gt; Starting values for parameters to be optimised:
+#&gt; value type
+#&gt; parent_0 100.7500 state
+#&gt; k_parent_sink 0.1000 deparm
+#&gt; k_parent_m1 0.1001 deparm
+#&gt; k_m1_sink 0.1002 deparm
+#&gt;
+#&gt; Starting values for the transformed parameters actually optimised:
+#&gt; value lower upper
+#&gt; parent_0 100.750000 -Inf Inf
+#&gt; log_k_parent_sink -2.302585 -Inf Inf
+#&gt; log_k_parent_m1 -2.301586 -Inf Inf
+#&gt; log_k_m1_sink -2.300587 -Inf Inf
+#&gt;
+#&gt; Fixed parameter values:
+#&gt; value type
+#&gt; m1_0 0 state
+#&gt;
+#&gt; Optimised, transformed parameters with symmetric confidence intervals:
+#&gt; Estimate Std. Error Lower Upper
+#&gt; parent_0 99.600 1.61400 96.330 102.900
+#&gt; log_k_parent_sink -3.038 0.07826 -3.197 -2.879
+#&gt; log_k_parent_m1 -2.980 0.04124 -3.064 -2.897
+#&gt; log_k_m1_sink -5.248 0.13610 -5.523 -4.972
+#&gt;
+#&gt; Parameter correlation:
+#&gt; parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
+#&gt; parent_0 1.00000 0.6075 -0.06625 -0.1701
+#&gt; log_k_parent_sink 0.60752 1.0000 -0.08740 -0.6253
+#&gt; log_k_parent_m1 -0.06625 -0.0874 1.00000 0.4716
+#&gt; log_k_m1_sink -0.17006 -0.6253 0.47163 1.0000
+#&gt;
+#&gt; Residual standard error: 3.211 on 36 degrees of freedom
+#&gt;
+#&gt; Backtransformed parameters:
+#&gt; Confidence intervals for internally transformed parameters are asymmetric.
+#&gt; t-test (unrealistically) based on the assumption of normal distribution
+#&gt; for estimators of untransformed parameters.
+#&gt; Estimate t value Pr(&gt;t) Lower Upper
+#&gt; parent_0 99.600000 61.720 2.024e-38 96.330000 1.029e+02
+#&gt; k_parent_sink 0.047920 12.780 3.050e-15 0.040890 5.616e-02
+#&gt; k_parent_m1 0.050780 24.250 3.407e-24 0.046700 5.521e-02
+#&gt; k_m1_sink 0.005261 7.349 5.758e-09 0.003992 6.933e-03
+#&gt;
+#&gt; Chi2 error levels in percent:
+#&gt; err.min n.optim df
+#&gt; All data 6.398 4 15
+#&gt; parent 6.827 3 6
+#&gt; m1 4.490 1 9
+#&gt;
+#&gt; Resulting formation fractions:
+#&gt; ff
+#&gt; parent_sink 0.4855
+#&gt; parent_m1 0.5145
+#&gt; m1_sink 1.0000
+#&gt;
+#&gt; Estimated disappearance times:
+#&gt; DT50 DT90
+#&gt; parent 7.023 23.33
+#&gt; m1 131.761 437.70
+#&gt; </div><div class='input'>
+<span class='co'>## Not run: ------------------------------------</span>
+<span class='co'># fit.2 &lt;- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE)</span>
+<span class='co'># summary(fit.2, data=FALSE) </span>
+<span class='co'>## ---------------------------------------------</span>
+
+<span class='no'>initials</span> <span class='kw'>&lt;-</span> <span class='no'>fit</span>$<span class='no'>start</span>$<span class='no'>value</span>
+<span class='fu'>names</span>(<span class='no'>initials</span>) <span class='kw'>&lt;-</span> <span class='fu'>rownames</span>(<span class='no'>fit</span>$<span class='no'>start</span>)
+<span class='no'>transformed</span> <span class='kw'>&lt;-</span> <span class='no'>fit</span>$<span class='no'>start_transformed</span>$<span class='no'>value</span>
+<span class='fu'>names</span>(<span class='no'>transformed</span>) <span class='kw'>&lt;-</span> <span class='fu'>rownames</span>(<span class='no'>fit</span>$<span class='no'>start_transformed</span>)
+<span class='fu'>transform_odeparms</span>(<span class='no'>initials</span>, <span class='no'>SFO_SFO</span>)</div><div class='output co'>#&gt; parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
+#&gt; 100.750000 -2.302585 -2.301586 -2.300587
+#&gt; </div><div class='input'><span class='fu'>backtransform_odeparms</span>(<span class='no'>transformed</span>, <span class='no'>SFO_SFO</span>)</div><div class='output co'>#&gt; parent_0 k_parent_sink k_parent_m1 k_m1_sink
+#&gt; 100.7500 0.1000 0.1001 0.1002
+#&gt; </div><div class='input'>
+<span class='co'>## Not run: ------------------------------------</span>
+<span class='co'># # The case of formation fractions</span>
+<span class='co'># SFO_SFO.ff &lt;- mkinmod(</span>
+<span class='co'># parent = list(type = "SFO", to = "m1", sink = TRUE),</span>
+<span class='co'># m1 = list(type = "SFO"),</span>
+<span class='co'># use_of_ff = "max")</span>
+<span class='co'># </span>
+<span class='co'># fit.ff &lt;- mkinfit(SFO_SFO.ff, FOCUS_2006_D)</span>
+<span class='co'># summary(fit.ff, data = FALSE)</span>
+<span class='co'># initials &lt;- c("f_parent_to_m1" = 0.5)</span>
+<span class='co'># transformed &lt;- transform_odeparms(initials, SFO_SFO.ff)</span>
+<span class='co'># backtransform_odeparms(transformed, SFO_SFO.ff)</span>
+<span class='co'># </span>
+<span class='co'># # And without sink</span>
+<span class='co'># SFO_SFO.ff.2 &lt;- mkinmod(</span>
+<span class='co'># parent = list(type = "SFO", to = "m1", sink = FALSE),</span>
+<span class='co'># m1 = list(type = "SFO"),</span>
+<span class='co'># use_of_ff = "max")</span>
+<span class='co'># </span>
+<span class='co'># </span>
+<span class='co'># fit.ff.2 &lt;- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D)</span>
+<span class='co'># summary(fit.ff.2, data = FALSE)</span>
+<span class='co'>## ---------------------------------------------</span></div></pre>
+ </div>
+ <div class="col-md-3">
+ <h2>Author</h2>
+
+ Johannes Ranke
+
+ </div>
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